Evaluate ∫$$exe2x+6ex+5dx$$

Correct option is 114log⁡ex+1ex+5+C

Questions

$Evaluate \int \frac{e^{x}}{e^{2 x} + 6 e^{x} + 5} d x$

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14log⁡ex+1ex+5+C

14log⁡ex+2ex+4+C

14log⁡ex+5ex+1+C

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detailed solution

Correct option is A

I=∫exe2t+6ex+5dx=∫exex2+6ex+5dx Let ex=t⇒exdx=dt∴ I=∫dtt2+6t+5=∫1(t+3)2−22dt =12⋅2log⁡t+3−2t+3+2+C=14log⁡ex+1ex+5+C

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Evaluate ∫exe2x+6ex+5dx

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$Evaluate \int \frac{e^{x}}{e^{2 x} + 6 e^{x} + 5} d x$